Superpotential for novel symmetry beyond shape invariance

2022/05/28 by Dong, Shi-Hai, Rath, Biswanath
#FOS: Physical sciences #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2206.00043

Abstract

We propose a new "superpotential" and find that neither the supersymmetric energy conditions nor the associated shape invariance condition remain valid. On the other hand a new energy condition E_n⁺-E_n^(-)=2 between the two partner Hamiltonian H^(±) emerges. Mathematical proof supported the present findings with examples are presented. It is observed that, when the superpotential is associated with discontinuity or distortion, SUSY energy conditions and the shape invariance condition will no longer hold good.

Related

• Ab Initio Method for Obtaining Exactly Solvable Quantum Mechanical Potentials
• A Unified Scheme of Central Symmetric Shape-Invariant Potentials
• Remark on Shape Invariant Potential
• Solvable Schrodinger Equations of Shape Invariant Potentials Having Superpotential W(x,A,B)=Atanh(px)+Btanh(6px)
• SWKB and proper quantization conditions for translationally shape invariant potentials